docs: point-source solved-variant guides (phase 4 of #657)

[Jammy2211]

Summary

Phase 4 (guides/docs) of the point-source solved-likelihood series (PyAutoLens#657; library API merged in phase 2 via PyAutoArray#414 / PyAutoGalaxy#531 / PyAutoLens#659). Documents the full likelihood-option matrix — pairing scheme × centre treatment (free vs analytically solved) — across the workspace guides:

• The pairing guide now carries the deep prose: the al.ps.PointSolved / SolvedCentre variant matrix, the tensor-weighted source-plane chi-squared (Lombardi 2024, arXiv:2406.15280 §5.1) and its weighting = "jacobian" | "magnification" conventions, the solved flux/time-delay fits, the missing-image-penalty status, and a runnable solved-centre demo case.
• Fixes the false claim in cluster/likelihood_function.py that FitPositionsSource(profile=None) uses a back-traced barycenter (it raises) — the real centre-free option is al.ps.PointSolved + FitPositionsSourceSolved.
• Writes the deferred cluster-scale recommendation from the phase-3 profiling numbers (analytic β* ≈ timing-noise overhead, −2 free parameters per point source): search with FitPositionsSourceSolved, validate with the image-plane chi-squared. Demonstrated defaults in the modeling scripts are unchanged (prose-only recommendation).
• Attribution: image-plane solved variants are a PyAutoLens extension with glafic precedent (Oguri 2010) and are not attributed to Lombardi 2024; the paper is cited only for the solved source-plane/flux/time results.

Scripts Changed

• scripts/guides/point_source_pairing.py — second-axis sections (solved-variant matrix, tensor-vs-scalar weighting, solved fluxes/delays, missing-image penalty, cluster recommendation) + runnable Case 4 solved-centre demo
• scripts/point_source/fit.py — __Solved Source Centre__ section with a runnable FitPositionsSourceSolved fit; defaults note (FitPointDataset → FitPositionsImagePair vs AnalysisPoint → FitPositionsImagePairRepeat); solved flux/time-delay pointers
• scripts/cluster/likelihood_function.py — profile=None false claim replaced with the real solved-centre option; when-to-use advice updated to the solved search-stage recommendation; header notes the *Solved siblings
• scripts/point_source/features/fluxes.py — __Analytic Flux (Solved)__ compose-only section (fit_flux_cls=al.FitFluxesSolved; model drops from N=8 to N=5)
• scripts/point_source/features/time_delays.py — __Analytic Reference Time (Solved)__ compose-only section (fit_time_delays_cls=al.FitTimeDelaysSolved)
• scripts/point_source/modeling.py, scripts/cluster/modeling.py, scripts/cluster/start_here.py — short centre-free mentions where model composition is discussed
• scripts/cluster/lenstool/modeling.py — Lenstool-mapping table note: FitPositionsSourceSolved with weighting="magnification" matches Lenstool's scalar µ² convention

Notebooks regenerated for all nine touched scripts; generator artifacts (workspace_index.json, llms-full.txt, .script_sizes.json) refreshed.

Upstream PR

PyAutoLabs/PyAutoLens#659 (MERGED 2026-07-27)

Test Plan

• Four code-changed scripts executed locally (pairing guide + point_source/fit.py plain; features/fluxes.py + features/time_delays.py under the smoke profile) — all pass; solved centre recovers the true (0.07, 0.07)
• check_sizes.sh clean; notebook regeneration is 1:1 with touched scripts, no stray diffs
• Smoke tests pass for all affected workspaces

Generated by the PyAutoLabs agent workflow.